Position change of body in non-isolated system

[meathead]

Homework Statement

A body of mass 5 kg is initially at rest. At time t=0, a constantly increasing force is applied to the body for 7.5 seconds according to:F(t)=at; where a is a constant 0.866 N/s. Determine the distance x the body travels during the application of the force.

Homework Equations

delta E of system = sigma T
sum of forces in y direction =0
normal force - mass*gravitational acceleration=0
work=force*change in position
1/2mass*final velocity^2 = 1/2mass*initial velocity^2 + work

The Attempt at a Solution

At kind of a loss for where to start this problem because the force is not constant.
Can I some how find a value for Work and use that to solve for final velocity and use that to find change in position? Please Help!

 

[ehild]

You can not use the work-energy theorem in this problem.
Use Newton's Law: the acceleration is force/mass. Now the acceleration depends on time. Acceleration is the time derivative of velocity; you get velocity by integrating acceleration:

$$v(t) = \int{a(t)dt}$$

the integration constant is detemined from the condition v(0)=0.
Velocity is the time derivative of displacement: you get the displacement by integrating velocity: v(t)

$$x(t=7.5) -x(0) = \int_0^{t=7.5}{v(t)dt}$$



ehild